What a GIF file actually is
GIF dates to 1987 and stores at most 256 colours from a palette, compressed losslessly with LZW. Transparency is a single on/off flag on one palette entry rather than a real alpha channel, which is why GIF edges against a coloured background look jagged.
GIFs come from the reaction-image corner of the internet, from old web assets, and from screen recorders that default to it. Anything animated and low-colour that has been passed around for years is probably still a GIF.
What you get from ICO
ICO is a container that holds one or more small square images, with transparency, for use as an icon. It caps out at 256×256 — anything larger has to be scaled down, and the format is not intended for general pictures.
Every browser requests /favicon.ico by default, with no HTML required, and Windows uses ICO for application and shortcut icons. It is a narrow format that is completely reliable inside its niche.
What changes when you convert GIF to ICO
Both formats are lossless, so nothing is thrown away in either direction — this is a container change rather than a quality decision. What differs is how efficiently each one packs the same pixels, and how widely each is supported by the software you need to open it in.
Transparency technically survives, but it improves on the way. GIF has no alpha channel — just one palette entry flagged as transparent — which is why GIF cut-outs have hard, jagged edges. ICO stores a full 8-bit alpha, so anything you composite afterwards can have genuinely smooth edges, even though the original's jaggedness is baked in.
Only the first frame survives. GIF is the one source here that can be animated, and ICO output is a still image, so an animated GIF converts to its opening frame. The upside for static GIFs is real: escaping the 256-colour palette removes the banding, and the file usually gets smaller at the same time.
ICO cannot exceed 256×256, so anything larger is scaled down to fit while keeping its aspect ratio. Work from a square source if you can — a wide image gets letterboxed into the square, and fine detail disappears entirely at the 16-pixel size a browser tab actually renders.
An old GIF is a plausible icon source precisely because it is already small and low-colour. The catch is the hard-edged transparency: GIF's single transparent colour leaves jagged edges that become obvious once the icon sits on a dark background.